# Paraphrase and Solve: Exploring and Exploiting the Impact of Surface Form on Mathematical Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2404.11500 · HTML: https://mlsanity.com/paper/2404.11500/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 16 of its 28 references that are in the map.
- First posted on arXiv 17 Apr 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 16 of 16)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Chameleon: Plug-and-Play Compositional Reasoning with Large Language Models](https://mlsanity.com/paper/2304.09842/) (2023)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [AutoPrompt: Eliciting Knowledge from Language Models with Automatically Generated Prompts](https://mlsanity.com/paper/2010.15980/) (2020)
- [Demystifying Prompts in Language Models via Perplexity Estimation](https://mlsanity.com/paper/2212.04037/) (2022)
- [Holistic Evaluation of Language Models](https://mlsanity.com/paper/2211.09110/) (2022)
- [Joint Prompt Optimization of Stacked LLMs using Variational Inference](https://mlsanity.com/paper/2306.12509/) (2023)

## Built on by (most cited first, 14 of 14)

- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Self-Harmony: Learning to Harmonize Self-Supervision and Self-Play in Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.01191/) (2025)
- [Bridging Language Models and Financial Analysis](https://mlsanity.com/paper/2503.22693/) (2025)
- [Uncertainty Profiles for LLMs: Uncertainty Source Decomposition and Adaptive Model-Metric Selection](https://mlsanity.com/paper/2505.07309/) (2025)
- [AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking](https://mlsanity.com/paper/2506.07751/) (2025)
- [Your Language Model May Think Too Rigidly: Achieving Reasoning Consistency with Symmetry-Enhanced Training](https://mlsanity.com/paper/2502.17800/) (2025)
- [Clarification as Supervision: Reinforcement Learning for Vision-Language Interfaces](https://mlsanity.com/paper/2509.26594/) (2025)
- [Finding the Cracks: Improving LLMs Reasoning with Paraphrastic Probing and Consistency Verification](https://mlsanity.com/paper/2602.11361/) (2026)
- [Are We Evaluating Knowledge or Phrasing? Mitigating MCQA Sensitivity with ParaEval](https://mlsanity.com/paper/2606.10657/) (2026)
- [Same Question, Different Answers: Evaluating LLM Reliability Beyond Accuracy](https://mlsanity.com/paper/2607.22554/) (2026)
- [StoryCoder: Narrative Reformulation for Structured Reasoning in LLM Code Generation](https://mlsanity.com/paper/2604.14631/) (2026)
- [When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scaling](https://mlsanity.com/paper/2604.26644/) (2026)
- [Representation Robustness Under Executable Reasoning Constraints in Large Language Models for Mathematical Problem Solving](https://mlsanity.com/paper/2607.20520/) (2026)
- [Test-Time Augmentation for LLMs: When Input Diversity Beats Output Diversity at Matched Compute](https://mlsanity.com/paper/2608.09351/) (2026)

## Abstract (arXiv)

This paper studies the relationship between the surface form of a mathematical problem and its solvability by large language models. We find that subtle alterations in the surface form can significantly impact the answer distribution and the solve rate, exposing the language model's lack of robustness and sensitivity to the surface form in reasoning through complex problems. To improve mathematical reasoning performance, we propose Self-Consistency-over-Paraphrases (SCoP), which diversifies reasoning paths from specific surface forms of the problem. We evaluate our approach on four mathematics reasoning benchmarks over three large language models and show that SCoP improves mathematical reasoning performance over vanilla self-consistency, particularly for problems initially deemed unsolvable. Finally, we provide additional experiments and discussion regarding problem difficulty and surface forms, including cross-model difficulty agreement and paraphrasing transferability, and Variance of Variations (VOV) for language model evaluation.